Simplify the following expression: $ q = \dfrac{z + 9}{5z - 3} + 10 $
Answer: In order to add expressions, they must have a common denominator. Multiply the second expression by $\dfrac{5z - 3}{5z - 3}$ $ \dfrac{10}{1} \times \dfrac{5z - 3}{5z - 3} = \dfrac{50z - 30}{5z - 3} $ Therefore $ q = \dfrac{z + 9}{5z - 3} + \dfrac{50z - 30}{5z - 3} $ Now the expressions have the same denominator we can simply add the numerators: $q = \dfrac{z + 9 + 50z - 30}{5z - 3} $ $q = \dfrac{51z - 21}{5z - 3}$